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 chris December 19, 2003 11:46

help! flow in square duct

I am an academic in the UK and I have constructed a kinetic instrument that uses a small flow channel 0.25 mm square. This channel is imaged during steady state flow conditions using a CCD. I know the volume comming through the channel per unit time (around 1 mL per second and so I can calculate the linear velocity of the solution in the flow channel. When I use this linear velocity to generate my time base, I get an error of 1.3 in my kinetic rates compared with other measurements. This assumes the flowing channel cross section is 0.25 x 0.25 mm, i.e. 0.0625 mm ^3. However if I assume a flowing channel of diameter 0.25 mm I get the correct answer!! Is there any way of simulating flow in this channel and showing that the corner quadrants are static, i.e. that the true flow is down a 0.25 mm diameter cylinder in the middle?

Any help would be appreciated as I am a biologist!!

 Jim Park December 19, 2003 18:18

Re: help! flow in square duct

What do you mean by 'linear velocity'? The most obvious velocity is usually called the 'bulk velocity' and is calculated from V = (volume flow rate)/(cross sectional area).

The maximum velocity in a cross section will be greater than V and will occur somewhere away from the walls of the channel. I think you could calculate the exact magnitude and location for a fluid of constant viscosity in laminar flow using an undergraduate fluids text and a calculator. However, I can't think of many 'biological' fluids with a constant viscosity.

The maximum occurs because the fluid 'sticks' to the walls - that is, it has zero velocity right at the wall. So the corners of your channel have areas of very low velocity because two walls have a major slowing effect. Note as well that you'll have a different flow for an open (3-walled) channel than from a closed (4-walled) channel.

If your calibration/correlation coefficient depends on the maximum velocity on a cross section and you're using a bulk velocity to calculate the coefficient, an error of 1.3 seems plausible. [For an academic 2-dimensional case, Vmax/Vbulk = 1.5].

To answer more directly, assuming you know the viscosity of your fluid, you can calculate the details of the velocity in the channel, analytically for an 'easy' viscosity, numerically for a known viscosity function.

However, if you have a friend on the engineering faculty at your institution, you might consider buying him a pint and asking him about your problem! : )

Good luck!

 chris December 22, 2003 11:13

Re: help! flow in square duct

Dear Jim